Exhaust system and method of estimating diesel particulate filter soot loading for same

ABSTRACT

A method of estimating soot loading in a diesel particulate filter (DPF) in a vehicle exhaust system includes determining engine operating conditions of an engine in exhaust flow communication with the diesel particulate filter, and monitoring a pressure differential of the exhaust flow across the diesel particulate filter. The method includes estimating soot loading in the diesel particulate filter according to a pressure-based model using the monitored pressure differential when the engine operating conditions are within a predetermined first set of engine operating conditions, and estimating soot loading in the diesel particulate filter according to an engine-out soot model and a DPF soot loading model when the engine operating conditions are within a predetermined second set of operating conditions. The method includes updating the engine-out soot model based in part on a difference in estimated soot loading between the pressure-based model and the DPF soot loading model.

TECHNICAL FIELD

The present teachings generally include a method of estimating soot loading in a diesel particulate filter and an exhaust system implementing the method.

BACKGROUND

Diesel particulate filters (DPFs) are designed to remove soot from the exhaust flow of a diesel engine. When the accumulated soot reaches a predetermined amount, the filter is “regenerated” by burning off the accumulated soot. There is no mechanism available to directly measure the amount of soot in the exhaust flow from the engine, or to directly measure the amount of soot in the DPF when the vehicle is in use. Accordingly, mathematical and empirical soot models have been used to estimate the amount of soot present in the filter so that timely disposal or regeneration of the filter can be assured. Modeling the exhaust flow and resultant DPF loading is dependent on complex chemical reactions and physical flow dynamics. One mathematical soot model is dependent on engine operating conditions and an engine-out soot rate resulting from the engine operating conditions. Another soot model estimates the amount of soot in the filter based on the pressure drop in exhaust flow through the filter (i.e., a differential pressure across the filter). This soot model is thus based partly on a measured parameter (pressure differential). Accuracy of the soot model used is important, as the DPF functions optimally when the amount of soot present is below a predetermined amount. An accurate soot model ensures that the DPF is not regenerated unnecessarily at relatively low soot concentrations (grams of soot per volume of filter), thus enhancing fuel economy.

SUMMARY

A DPF soot loading estimate using a mathematical model implemented by an onboard computer as an algorithm can be less expensive than measurement-based models that require numerous and/or expensive sensing devices, and can be used under a greater range of operating conditions than a measurement-based system. The accuracy of such a mathematical model can be improved if the model is updated by comparison of a model-based result with a measurement-based result, such as the pressure-based model. However, accurate DPF soot loading has been determined from offboard testing, in which the DPF is periodically removed from the exhaust system and weighed,—since the pressure-based model is only an accurate predictor of soot loading under certain engine operation conditions, such as high speed steady driving.

A method of estimating soot loading is presented that enables reliance on a mathematical soot loading model, referred to herein as a DPF soot loading model, by updating an engine-out soot rate used in the mathematical model based on a differential pressure-based model under all engine operating conditions. A method of estimating soot loading in a DPF in a vehicle exhaust system includes determining engine operating conditions of an engine in exhaust flow communication with the diesel particulate filter, and monitoring a pressure differential of the exhaust flow across the diesel particulate filter. The method includes estimating soot loading in the diesel particulate filter according to a pressure-based model using the monitored pressure differential when the engine operating conditions are within a predetermined first set of engine operating conditions (defining an enable mode), and estimating soot loading in the diesel particulate filter according to an engine-out soot model and a DPF soot loading model when the engine operating conditions are within a predetermined second set of operating conditions (defining a disable mode). In both cases, the estimating is via an electronic controller. The engine-out soot model and the DPF soot loading model are stored on the electronic controller. The engine-out soot model is based on the engine operating conditions, and the DPF soot loading model is based at least partially on the engine-out soot model.

The method includes updating the engine-out soot model based in part on a difference in estimated soot loading between the pressure-based model and the DPF soot loading model. Updating the engine-out soot model is done in real time during the enable mode. As used herein, updating in “real time” means updating the engine-out soot model based on the difference without first requiring the occurrence of a subsequent event or condition. Updating the engine-out soot model is done after a return to engine operating conditions within the enable mode after operation in the disable mode, and is based in part on a saved estimated soot rate loading value from an engine operating point in the enable mode prior to the operation in the disable mode. That is, updating is not in real time during the disable mode, and instead occurs only after a return to the enable mode, when a pressure-differential measurement is again considered to be sufficiently indicative of soot loading.

The above features and advantages and other features and advantages of the present teachings are readily apparent from the following detailed description of the best modes for carrying out the present teachings when taken in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of a vehicle exhaust system including a diesel particulate filter and a controller.

FIG. 2 is a schematic diagram of the controller of FIG. 1, including a processor with an engine-out soot model, a DPF soot loading model based partly on the engine-out soot model, a DPF soot loading pressure-based model, and a learning algorithm for the engine-out soot model.

FIG. 3 is a schematic three-dimensional plot of engine-out soot rate, showing engine-out soot rate at various engine operating points according to engine speed and quantity of fuel injected, and associated current and updated engine-out soot rate values at predetermined engine operating points.

FIG. 4 is a schematic illustration of a soot rate table showing engine-out soot rate as a function of engine speed and injected fuel quantity rate, and showing updated engine-out soot rate values for various engine operating conditions.

FIG. 5 is a schematic three-dimensional plot of operation time at various engine operating points according to engine speed and injected fuel quantity rate, and the distribution of operation at one engine operating point to predetermined engine operating points

FIG. 6 is a schematic illustration of a time table showing an engine operating point and the distribution of operation time at predetermined engine operating points having various engine speeds and at different injected fuel quantity rates.

FIG. 7 is a schematic flow diagram of a method of estimating soot loading carried out by the controller of FIG. 1 via the models and learning algorithm of FIG. 2.

DETAILED DESCRIPTION

Referring to the drawings, wherein like reference numbers refer to like components throughout the several views, FIG. 1 shows a vehicle 10 that includes an engine 11 with a representative exhaust system 12 that includes a diesel particulate filter (DPF) 14. A monitoring system 16 for the DPF 14 is operable to monitor the amount of soot mass in the DPF 14 in order to ensure filter performance, enhance overall fuel economy and reduction of emissions, and provide for timely regeneration of the DPF 14.

The exhaust system 12 includes a diesel oxidation catalyst 18 that oxidizes and burns hydrocarbons in the exhaust flow 20 exiting the engine 11. Exhaust then flows through a selective catalytic reduction catalyst 22, which converts at least some of the nitrogen oxides in the exhaust flow 20 into water and nitrogen. Exhaust then flows from an inlet 24 of the DPF 14 to an outlet 26 of the filter 14, and then exits the exhaust system 12. The exhaust system 12 may instead be arranged with the selective catalytic reduction catalyst 22 downstream of the DPF 14 without affecting the function of the monitoring system 16.

The monitoring system 16 includes a controller 28 that has a processor 30 that executes stored algorithms from a tangible, non-transitory memory, as described further with respect to FIG. 2 to estimate the amount of soot in the DPF 14 and output a control signal 38 that causes engine operation at conditions (such as increased fuel amount) that initiate regeneration of the DPF 14. If the DPF 14 is a type that is actively regenerated by changing operating parameters to increase exhaust flow temperature to burn the soot, the signal 38 may affect engine parameters to cause the increase in temperature of the exhaust flow 20.

Data reflecting real-time operating parameters in the exhaust system 12 is input into the controller 28 and used by various ones of the stored algorithms as described herein. For example, the monitoring system 16 may include an engine speed sensor 32 positioned in operative communication with the engine crankshaft 34 and operable to monitor engine speed 36 (also referred to as a first engine operating condition) such as in revolutions per minute (rpm) and provide a signal representing engine speed to the processor 30. Additionally, the monitoring system 16 includes a sensor 37 that measures air fuel ratio in the engine 11 and provides an air fuel ratio 42 via a signal to the processor 30. The monitoring system 16 also includes a sensor 39 that measures air flow into the engine 11 and provides an air flow measurement 43 via a signal to the controller 28. A fuel flow measuring device 49 measures an injected fuel quantity rate 47 (also referred to as a second engine operating condition) such as the fuel flow in cubic millimeters per engine stroke (mm³/cycle) into a fuel injection system for the engine 11. The fuel quantity rate 47 is provided as a signal to the processor 30. Fuel quantity rate 47 is proportional to engine load (e.g., torque at the crankshaft 34). Additional engine operating parameters and exhaust system 12 operating parameters can also be provided to the controller 28 and used by the stored algorithms on the processor 30 to estimate the amount of soot loading in the DPF 14. For example, exhaust temperature and other parameters can be monitored.

The monitoring system 16 also includes a differential pressure measurement device 44 that is operable to measure a third operating parameter, which is a pressure differential between exhaust flow at the inlet 24 and exhaust flow at the outlet 26 of the DPF 14. The differential pressure measurement device 44 is in fluid communication with the exhaust flow 20 at the inlet 24 and at the outlet 26 and emits a signal representative of a differential pressure 46 (also referred to as a pressure drop). The differential pressure 46 is utilized by the processor 30 as further described below.

Referring to FIG. 2, the processor 30 is shown in more detail to represent the algorithms executed by and the empirical data accessed by the processor 30. The processor 30 includes a first stored algorithm, also referred to as a DPF soot loading pressure-based model 50, that provides an inferred DPF soot loading estimate based in part on the differential pressure 46 provided by the pressure measurement device 44. The engine operating conditions 36, 47 are also provided to the pressure-based model 50. The pressure-based model 50 represents the dynamics of engine-out soot and DPF soot loading inferred from the pressure differential across the DPF 14. The pressure-based model 50 can include stored data based on prior testing, including offline weighings of the DPF 14 that are coordinated with measured pressure differentials and engine operating conditions.

The processor 30 includes a second stored algorithm, also referred to as a DPF soot loading model 52 that provides an estimated DPF soot loading based on a mathematical model of the DPF kinetic process. The mathematical model is dependent on the engine operating conditions 36, 47, as well as an estimated engine-out soot rate 53 provided as a signal from an engine-out soot model 54. The engine-out soot model 54 is an input to the DPF soot loading model 52, as it provides an estimated engine-out soot rate 53 used by the DPF soot loading model 52. The engine-out soot model 54 is a group of stored lookup tables of engine-out soot rate values correlated with the selected engine operating points. An engine operating point is represented by an engine speed and by an injected fuel quantity rate in grams.

Finally, a learning algorithm 56 is utilized that provides an output 59 that is an adaptation of the engine-out soot model 54 to update the engine-out soot model 54 under all engine operating conditions using a comparison of the estimated soot loading by the pressure-based model 50 and the estimated soot loading by the DPF soot loading model 52. By updating the engine-out soot model 54 under all engine operating conditions based on this comparison, the DPF soot loading model 52 can provide a more accurate estimated DPF soot loading estimate adapting to different engine operation conditions. The pressure-based model 50 more accurately reflects actual DPF soot loading than does the DPF soot loading model 52 under a first set of engine operating conditions (the enable mode), and can thus be used as a check to update the DPF soot loading model 52. However, the pressure-based model 50 is less accurate under other engine operating conditions (a second set of engine operating conditions called the disable mode). For example, at low engine speeds, or non-steady (transient) driving, the differential pressure 46 is less correlated with DPF soot loading than at high-speed, steady driving.

The learning algorithm 56 enables the engine-out soot model 54 to be updated to reflect engine operation in the disable mode as well as in the enable mode, as described herein. In other words, the learning algorithm 56 extends updating of the engine-out soot model 54 and the DPF soot loading model 52 to an entire engine operating range (which is defined as the total of the first set of engine operating conditions and the second set of engine operation conditions). The learning algorithm 56 continuously adapts the engine-out soot model 54 and the DPF soot loading model 52 to the pressure-based model 50.

The learning algorithm 56 thus operates in one of two different operating modes: the disable mode or the enable mode, dependent on the engine operating conditions. In the disable mode, measurement of the pressure differential 46 is relatively inaccurate. The disable mode is defined as the engine operating conditions 36, 47 being within the second set of engine operating conditions. In the disable mode, there is no real-time learning for (i.e., updating of) the engine-out soot model 54. The second set of engine operating conditions reflects low speed driving and/or start-stop driving. In the enable mode, the measured differential pressure 46 is relatively accurate, and the learning algorithm 56 provides real-time learning of the engine-out soot model 54 as described herein. The learning algorithm 56 determines and saves certain operating parameters during the disable mode, and then updates the engine-out soot model 54 based on the saved operating parameters when the engine operating conditions return to the enable mode. Accordingly, the learning algorithm 56 is effective to update the engine-out soot model 54 for all engine operating conditions, either in real time or at a later time, as described herein.

The learning algorithm 56 accomplishes different tasks depending on whether it is in the enable mode, the disable mode, or transitioning from the disable mode to the enable mode. These tasks are described in detail herein, and are included in the method of estimating DPF soot loading 100 carried out by the controller 28 and the processor 30 thereon, as schematically illustrated in FIG. 7. In a first step 102, the controller 28 monitors engine operating conditions, including engine speed 36 and fuel quantity rate 47. That is, the controller 28 tracks actual engine operating points within the range of engine operating conditions by periodically analyzing the engine speed 36 and fuel quantity rate 47 provided. The controller 28 also has a timer that measures the time of operation at each monitored engine operating point in step 104. The controller 28 also periodically monitors the pressure differential 46 provided by the pressure differential measurement device 44 in step 106. Steps 102, 104, 106 are repeated periodically throughout the method 100.

Based on the engine operating conditions determined in step 102, the processor 28 determines in step 108 whether the current engine operating conditions (i.e., the most recent monitored engine operating conditions) are within the first set of engine operating conditions. If the engine operating conditions are within the first set of engine operating conditions, then the learning algorithm 56 is in the enable mode, and the processor 30 accomplishes steps 110-120 as described herein.

In the enable mode, the differential pressure measurement 46 can be relied upon to accurately reflect the amount of accumulated soot in the DPF 14, and the pressure-based model 50 can thus be used to update the engine-out soot model 54 directly. Referring to FIG. 3, a lookup table 57 included in the engine-out soot model 54 stores engine-out soot rate 53 (in grams per second) according to engine speed 36 (in revolutions per minute) and fuel quantity rate 47 (mm³/cycle). Various current soot rate values 60 are indicated with open circles (i.e., the soot rate values at each engine operating point as stored in a lookup table 57 of the engine-out soot model 54 prior to updating). Only some of the current soot rate values 60 are labeled. The initial current soot rate values 60 are based on initial soot rate values determined during offline testing for a vehicle having the engine 11 and exhaust system 12, and are then updated during vehicle use according to the method 100 carried out by the processor 30 as described herein. Incremental soot rate values 62A, 62B, 62C as determined by the pressure-based model 50 at a series of actual engine operating points as periodically determined in step 102 are indicated in FIG. 3. The current stored soot rate values 60 in the lookup table of the engine-out soot model 54 are updated using each of the soot rate values 62A, 62B, 62C determined by the pressure-based model 50 as described herein.

The soot rate value 62A determined at an actual engine operating point P_(x,y) is used to provide updated engine-out soot rate values 64A, 64B, 64C, 64D, as shown above four corresponding current soot rate values 60 (i.e., the soot rate values for four engine operating conditions P1, P2, P3, P4 within a predetermined distance of the actual engine operating point P_(x,y) that corresponds with soot rate value 62A). The predetermined distance is the increment between adjacent stored engine speed 36 values and between adjacent stored fuel quantity rate 47 values in the lookup table 57, as further described with respect to FIG. 4. Current soot rate values 60 within a predetermined distance of the actual engine operating points corresponding with the engine-out soot rate values 62B, 62C would be updated in like manner. The updated values in table 57 will be used in the engine-out soot model 54 to calculate the estimated engine soot rate 53.

Referring again to FIG. 7, the main steps in the enable mode include step 110, calculating the inferred DPF soot loading {circumflex over (M)}_(Δp)(t) from the differential pressure 46 (ΔP) measurement via the pressure-based model 50.

In step 112, estimated DPF soot loading {circumflex over (M)}_(1dk)(t) is then calculated from the DPF soot loading model 52. A soot loading error {circumflex over (M)}(t) (also referred to as a soot loading difference) is then calculated in step 114 by subtracting the DPF soot loading model {circumflex over (M)}_(1dk)(t) from the inferred DPF soot loading {circumflex over (M)}_(Δp)(t):

Δ{circumflex over (M)}(t)={circumflex over (M)} _(Δp)(t)−{circumflex over (M)} _(1dk)(t)

Using the accumulated time T at the engine operating point (e.g., the point having the soot rate value 62A) as determined in step 104, the estimated soot rate error {circumflex over (Z)} (also referred to as a soot rate difference) is determined in step 116 by dividing the soot loading error {circumflex over (M)}(t) by the accumulated time T:

$\hat{Z} = \frac{\Delta {\hat{M}(t)}}{T}$

FIG. 4 shows a soot rate table as a two-dimensional plot of fuel quantity rate 47 on the Y-axis versus engine speed 36 on the X-axis. As illustrated in FIG. 4, current soot rate values 60 in the engine-out soot table 57 of FIG. 3 are updated by distributing the estimated soot rate error {circumflex over (Z)} to the soot rate values 60 at the four adjacent junction points of the engine-out soot table 57, based on respective distances between the current engine operation point (P_(x,y)) (corresponding to the operating point having the soot rate 62A) and the four adjacent junction points P1, P2, P3, P4. If the distance from the engine operating point P_(x,y) to its four adjacent junction points P1, P2, P3, P4 are d_(i,j), d_(i,j+1), d_(i+1,j), and d_(i+1,j+1) respectively, then these distances can be calculated in step 118 by the geometric distance formula for determining the distance between two points in a plane, e.g., for d_(i,j):

d _(i,j)=√{square root over ((x−i)²+(y−j)²)}{square root over ((x−i)²+(y−j)²)}.

The total distance d from the engine operating point P_(x,y) to these four adjacent points is:

d=d _(i,j) +d _(i,j+1) +d _(i+1,j) +d _(i+1,j+1).

Corresponding to the engine operating point P_(i,j), the current soot rates values 60 at each adjacent junction point in the engine-out soot rate table 57 (i.e., soot rate values 60 at time t−1) are updated to soot rate values 64A, 64B, 64C, 64D at time t by:

${{Z_{i,j}(t)} = {{Z_{i,j}\left( {t - 1} \right)} + {k\hat{Z}\frac{d_{i,j}}{d}}}};$ ${{Z_{i,{j + 1}}(t)} = {{Z_{i,{j + 1}}\left( {t - 1} \right)} + {k\hat{Z}\frac{d_{i,{j + 1}}}{d}}}};$ ${{Z_{{i + 1},j}(t)} = {{Z_{{i + 1},j}\left( {t - 1} \right)} + {k\hat{Z}\frac{d_{{i + 1},j}}{d}}}};{and}$ ${{Z_{{i + 1},{j + 1}}(t)} = {{Z_{{i + 1},{j + 1}}\left( {t - 1} \right)} + {k\hat{Z}\frac{d_{{i + 1},{j + 1}}}{d}}}};$

where 0≦k≦1 is a distribution gain determined by experiment to keep the learning process (i.e., the updating process) stable. Accordingly, the soot rate values 60 in the lookup table 57 are updated in step 120 via the output 59 by distributing the estimated engine out soot-rate error {circumflex over (Z)} in the lookup table 57 of FIG. 2 via soot rate error values that are calculated in proportion to the proximity of the engine operating points of the stored values (i.e., the current soot rate values 60) to the engine operating point at which the difference {circumflex over (M)}(t) is calculated. The method 100 then returns to step 108.

After steps 110 to 120, if it is then determined in step 108 that the engine operating conditions are in the disable mode, then at this transition from the enable mode to the disable mode, the learning algorithm 54 accomplishes steps 126-138 of the method 100. First, the method 100 moves to step 126 in which the last soot loading estimate based on the pressure-based model 50 during engine operation in the enable mode is saved. The last soot loading estimate based on the DPF soot loading model 52 during engine operation in the enable mode is saved in step 127.

Once in the disable mode, a lookup table 68 shown in FIG. 5 (named “Operation Time Table”) is constructed under the method 100 to record the engine operation time 70A, 70B, 70C at different engine operating points such as engine operating point P_(x,y) (shown in FIG. 6). Engine operation time 69 as determined in step 104 is stored according to engine speed 36 and fuel quantity rate 47. For example, at engine operating point P_(x,y) (e. g., corresponding with the engine operating point at which time 70A is spent), let the engine operation time be T_(x,y), and then T_(x,y) will be distributed and recorded at the four adjacent junction points PA, PB, PC, PD surrounding P_(x,y) as described below.

The four adjacent junction points in the Operation Time Table 68 are PA, PB, PC, PD (referred to as T_(i,j), T_(i,j+1), T_(i+1,j), and T_(i+1,j+1).) The distance from the engine operating point P_(x,y) to its four adjacent junction points P1, P2, P3, P4 is d_(i,j), d_(i,j+1), d_(i+1,j), and d_(i+1,j+1) respectively, and these distances can be calculated in step 128 by using the geometric distance formula for determining the distance between two points in a plane. For example, the distance d_(i,j) from point P_(x,y) to point P1 is:

d _(i,j)=√{square root over ((x−i)²+(y−j)²)}{square root over ((x−i)²+(y−j)²)}.

The total distance d from the engine operating point P_(x,y) to these four adjacent points is:

d=d _(i,j) +d _(i,j+1) +d _(i+1,j) +d _(i+1,j+1).

In step 130, the engine operation time 70A at the engine operating point P_(x,y) is distributed to the four adjacent engine operating points PA, PB, PC, PD according to the proximity of each of the four points to the engine operation point P_(x,y) at which the time 70A was measured. Then, corresponding to the engine operating point P_(x,y), the engine operation time distributed in step 130 at each adjacent point (i, j) in the Operation Time Table 68 is as follows:

${{T_{i,j}(t)} = {{T_{i,j}\left( {t - 1} \right)} + {k\mspace{11mu} T_{x,y}\frac{d_{i,j}}{d}}}};$ ${{T_{i,{j + 1}}(t)} = {{T_{i,{j + 1}}\left( {t - 1} \right)} + {k\mspace{11mu} T_{x,y}\frac{d_{i,{j + 1}}}{d}}}};$ ${{T_{{i + 1},j}(t)} = {{T_{{i + 1},j}\left( {t - 1} \right)} + {k\mspace{11mu} T_{x,y}\frac{d_{{i + 1},j}}{d}}}};{and}$ ${{T_{{i + 1},{j + 1}}(t)} = {{T_{{i + 1},{j + 1}}\left( {t - 1} \right)} + {k\mspace{11mu} T_{x,y}\frac{d_{{i + 1},{j + 1}}}{d}}}};$

where 0≦k≦1 is a distribution gain determined by experiment to keep the learning process (i.e., the updating) stable. The prior accumulated time 75 (if any) for operation during the second set of engine operating conditions at each of these points is shown with open circles in FIG. 5 (only one of which is labeled 75). The updated accumulated time 77A, 77B, 77C, 77D is shown at each point.

In step 131, it is then determined whether the engine operating conditions have returned to the enable mode. If they have not, then the method 100 returns to step 128 and continues to distribute time accumulated at a subsequent periodic engine operating point into the Operation Time Table 68 as described. When monitoring under step 131 indicates that engine operating conditions have returned to the enable mode, reliance on the pressure differential measurement 46 is resumed. The pressure-based model 50 is used to calculate the DPF soot accumulated during the time when the DPF ΔP measurement is disabled (i.e., during the disable mode). Soot loading determined to have occurred during the disable mode is distributed into each engine operating point during the disable mode according to the time spent thereon. In order to transition from the disable mode to the enable mode, in step 132, the soot loading increment error {circumflex over (M)}(t_(e)) (also referred to as a soot loading increment difference)

during the disable mode is calculated as follows:

Δ{circumflex over (M)}(t _(e))=[{circumflex over (M)} _(Δp)(t _(e))−{circumflex over (M)} _(Δp)(t _(d))]−[{circumflex over (M)} _(1dk)(t _(e))−{circumflex over (M)} _(1dk)(t _(d))];

where, referring to FIG. 2, {circumflex over (M)}_(1dk)(t_(e)) is the output of the DPF soot loading model 52, {circumflex over (M)}_(Δp)(t_(e)) is the output of the pressure-based model 50; and t_(d) and t_(e) are the time of entering the disable mode (i.e., time at the first recorded engine operating point in the second set of engine operating conditions as determined in step 108 after steps 110-112), and the time of entering the enable mode (i.e., time at the first recorded engine operating point in the first set of engine operating conditions after operation in the second set of engine operating conditions as determined in step 126), respectively.

Next, in step 134, the average total soot rate error M (also referred to as the average total soot rate difference) during the disable mode is calculated as follows:

${\Delta \overset{\_}{M}} = {\frac{\Delta {\hat{M}\left( t_{e} \right)}}{t_{e} - t_{d}}.}$

In step 136, the lookup table 57 of the engine-out soot model 54 is updated via the output 50 by soot rate error values that are calculated by distributing the average total soot rate error M to each junction point, where the accumulated time is recorded during the disable mode in the Operation Time Table 68, proportionally to the recorded accumulated time as an average soot rate error Z_(i,j)(t):

Z _(i,j)(t)=Z _(i,j)(t−1)+[T _(i,j) Δ M].

Finally, in step 138, the operation time table 68 is cleared so that it is ready for use during a subsequent occurrence of operating in the disable mode following operation in the enable mode. The method 100 then returns to step 108, with steps 102, 104, and 106 continuing periodically.

While the best modes for carrying out the many aspects of the present teachings have been described in detail, those familiar with the art to which these teachings relate will recognize various alternative aspects for practicing the present teachings that are within the scope of the appended claims. 

1. A method of estimating soot loading in a diesel particulate filter (DPF) in a vehicle exhaust system, the method comprising: determining engine operating conditions of an engine in exhaust flow communication with the diesel particulate filter; monitoring a pressure differential of the exhaust flow across the diesel particulate filter; estimating soot loading in the diesel particulate filter according to a pressure-based model using the monitored pressure differential when the engine operating conditions are within a predetermined first set of engine operating conditions; wherein said estimating is performed by an electronic controller; estimating soot loading in the diesel particulate filter according to an engine-out soot model and a DPF soot loading model when the engine operating conditions are within a predetermined second set of operating conditions; wherein said estimating is performed by the electronic controller; wherein said engine-out soot model and said DPF soot loading model are stored on the electronic controller; wherein the engine-out soot model is based on the monitored engine operating conditions and the diesel particulate soot loading model is based at least partially on the engine-out soot model; updating the engine-out soot model based in part on a difference in estimated soot loading between the pressure-based model and the DPF soot loading model; wherein said updating the engine-out soot model is performed by the electronic controller in real time when the engine operating conditions are within the first set of engine operating conditions; and wherein said updating the engine-out soot model is performed by the electronic controller after a return to engine operating conditions within the first set of engine operating conditions after operation in the second set of engine operating conditions, and is based in part on a saved estimated soot rate loading value from an engine operating point in the first set of engine operating conditions prior to said operation in the second set of engine operating conditions.
 2. The method of claim 1, wherein the engine-out soot model includes a lookup table of stored engine-out soot rate values correlated with the engine operating conditions; and wherein said updating the engine-out soot model in real time is by updating the stored engine-out soot rate values for a predetermined number of engine operating points within a predetermined proximity to the engine operating point at which said difference is calculated.
 3. The method of claim 2, further comprising: measuring time of operation at each engine operating point; calculating an estimated soot rate loading error; wherein the estimated soot rate loading error is said difference divided by a time of operation at the engine operating point at which said difference is calculated; wherein said updating the engine-out soot model in real time is by distributing a respective portion of said estimated soot rate loading error to each of said stored engine-out soot rate values of the predetermined number of engine operating points in the predetermined proximity to the engine operating point at which said difference is calculated; calculating a respective distance from each of the predetermined number of engine operating points to the engine operating point at which said difference is calculated; and wherein each respective portion is in proportion to each respective distance.
 4. The method of claim 1, further comprising: measuring time of operation at each engine operating point during the second set of engine operating conditions; calculating a respective distance from each of a predetermined number of engine operating points within a predetermined proximity to an engine operating point at which time is measured; and distributing the measured time at each engine operating point during the second set of engine operating conditions to each of the predetermined number of engine operating points within the predetermined proximity to the engine operating point at which time is measured; wherein said distributing is in proportion to the calculated respective distance.
 5. The method of claim 4, further comprising: calculating a total time between a last engine operating point in the first set of engine operating conditions prior to operation in the second set of engine operating conditions and a first engine operating point in the first set of engine operating conditions after a return from the second set of engine operating conditions; calculating a first difference between the estimated soot loading based on the pressure-based model and the estimated soot loading based on the DPF soot loading model, both measured at the first engine operating point in the first set of engine operating conditions after a return from the second set of engine operating conditions; calculating a second difference between the estimated soot loading based on the pressure-based model and the estimated soot loading based on the DPF soot loading model, both measured at the last engine operating point in the first set of engine operating conditions prior to operation in the second set of engine operating conditions; wherein the estimated soot loading based on the pressure-based model at the last engine operating point in the first set of engine operating conditions prior to operation in the second set of engine operating conditions is said saved estimated soot loading value; subtracting the second difference from the first difference to provide a soot loading increment error; dividing the soot loading increment error by the total time to provide an average total soot rate error; and wherein said updating after a return to engine operating conditions within the first set of engine operating conditions is by distributing the average total soot rate error to engine operating points in the second set of engine operating conditions in proportion to said distributed measured time.
 6. The method of claim 4, wherein the distributed measured time is saved in a time lookup table according to engine operating points within the second set of engine operating conditions, and further comprising: resetting the time lookup table to clear the distributed measured time following said updating after a return to engine operating conditions within the first set of engine operating conditions.
 7. The method of claim 1, wherein said monitoring engine operating conditions includes: monitoring engine speed; and estimating injected fuel rate.
 8. A method of estimating engine-out soot rate in exhaust flow from an engine, wherein engine-out soot flows from the engine to a diesel particulate filter (DPF), the method comprising: determining engine operating conditions; periodically determining via a controller whether a respective engine operating point in the engine operating conditions is within a first set of operating conditions or a second set of operating conditions; updating stored engine-out soot rate estimates via the controller by distributing a difference between a DPF pressure-based model and a DPF soot loading model according to respective proximities of a predetermined number of corresponding engine operating points to the respective engine operating point if the respective engine operating point is within the first set of operating conditions; wherein the pressure-based model is based on a measured pressure differential across the DPF; wherein the DPF soot loading model is based in part on the stored engine-out soot rate estimates; and updating the stored engine-out soot rate estimates via the controller by calculating an engine-out soot rate error based in part on a difference between the pressure-based model and the DPF soot loading model at (i) a final engine operating point within the first range of engine operating conditions immediately prior to one or more engine operating points within the second range of engine operating conditions, and at (ii) an initial engine operating point within the first range of engine operating conditions and subsequent to said one or more engine operating points within the second range of engine operating conditions; and distributing the calculated engine-out soot rate error via the controller according to a pro-rata portion of time spent at each engine operating point in the second range of operating conditions to a total time between the final engine operating point and the initial engine operating point.
 9. The method of claim 8, wherein the engine-out soot model includes a lookup table of stored engine-out soot rate values correlated with the engine operating conditions.
 10. The method of claim 8, wherein the pro-rata portion of time spent at each engine operating point in the second set of engine operating conditions is saved in a time lookup table according to engine operating points within the second set of engine operating conditions, and further comprising: resetting the time lookup table to clear the pro-rata portion of time following said updating after a return to engine operating conditions within the first set of engine operating conditions.
 11. The method of claim 8, wherein said determining engine operating conditions includes: monitoring engine speed; and estimating quantity of injected fuel quantity rate.
 12. An exhaust system for treating exhaust from an engine on a vehicle, the exhaust system comprising: a diesel particulate filter (DPF) in fluid communication with the engine; a differential pressure measurement device operatively connected to the DPF and operable to provide a signal corresponding with a pressure differential across the DPF; a controller in operative communication with the differential pressure measurement device to monitor the pressure differential and with the engine to monitor engine operating conditions; wherein the controller is configured to execute: a first stored algorithm that is a pressure-based model to provide an estimated soot loading in the DPF based on the pressure differential when engine operating conditions are within a first set of engine operating conditions; a second stored algorithm that is a DPF soot loading model based on the engine operating conditions and on an engine-out soot model when the engine operating conditions are within a second set of engine operating conditions; and a learning algorithm that updates the engine-out soot model based in part on a difference in estimated soot loading between the pressure-based model and the DPF soot loading model by updating the engine-out soot model (i) in real time when the engine operating conditions are within the first set of engine operating conditions, and (ii) after a return to engine operating conditions within the first set of engine operating conditions after operation in the second set of engine operating conditions; wherein updating after a return to engine operating conditions within the first set of engine operating conditions is based in part on a saved estimated soot rate loading value from an engine operating point in the first set of engine operating conditions prior to said operation in the second set of engine operating conditions.
 13. The exhaust system of claim 12, wherein the engine-out soot model includes a lookup table of stored engine-out soot rate values correlated with the engine operating conditions; and wherein said updating the engine-out soot model in real time is by updating the stored engine-out soot rate values for a predetermined number of engine operating points within a predetermined proximity to the engine operating point at which said difference is calculated.
 14. The exhaust system of claim 12, wherein the learning algorithm: measures time of operation at each engine operating point during the second set of engine operating conditions; calculates a respective distance from each of a predetermined number of engine operating points within a predetermined proximity to an engine operating point at which time is measured; and distributes the measured time at each engine operating point during the second set of engine operating conditions to each of the predetermined number of engine operating points within the predetermined proximity to the engine operating point at which time is measured and in proportion to the calculated respective distance.
 15. The exhaust system of claim 14, wherein the learning algorithm: calculates a total time between a last engine operating point in the first set of engine operating conditions prior to operation in the second set of engine operating conditions and a first engine operating point in the first set of engine operating conditions after a return from the second set of engine operating conditions; calculates a first difference between the estimated soot loading based on the pressure-based model and the estimated soot loading based on the DPF soot loading model, both measured at the first engine operating point in the first set of engine operating conditions after a return from the second set of engine operating conditions; calculates a second difference between the estimated soot loading based on the pressure-based model and the estimated soot loading based on the DPF soot loading model, both measured at the last engine operating point in the first set of engine operating conditions prior to operation in the second set of engine operating conditions; wherein the estimated soot loading based on the pressure-based model at the last engine operating point in the first set of engine operating conditions prior to operation in the second set of engine operating conditions is said saved estimated soot loading value; calculates a soot loading increment error by subtracting the second difference from the first difference; calculates an average total soot rate error by dividing the soot loading increment error by the total time; and wherein said updating after a return to engine operating conditions within the first set of engine operating conditions is by distributing the average total soot rate error to engine operating points in the second set of engine operating conditions in proportion to the distributed measured time.
 16. The exhaust system of claim 14, wherein the learning algorithm includes a time lookup table, and wherein the distributed measured time is saved in the time lookup table according to engine operating points within the second set of engine operating conditions; and wherein the learning algorithm resets the time lookup table to clear the distributed measured time following said updating after a return to engine operating conditions within the first set of engine operating conditions.
 17. The exhaust system of claim 12, wherein the engine operating conditions include engine speed and injected fuel quantity rate. 